Lemma 5.3  ([1]}).
If \(f\in W_0^{1,\Phi }(G)\) , then \(\Vert \cdot \Vert _{f,\phi }\)  defines a norm on the Banach space \((\mathbb {R}^n,\Vert \cdot \Vert _{f,\phi })\) . In particular, \(\Vert v\Vert _{f,\phi }>0\)  for any \(v\in S^{n-1}\) .

